Transposed Poisson structures on the Lie algebra of upper triangular matrices

We describe transposed Poisson structures on the upper triangular matrix Lie algebra Tₙ(F) , n>1 , over a field F of characteristic zero. We prove that, for n>2 , any such structure is either of Poisson type or the orthogonal sum of a fixed non-Poisson structure with a structure of Poisson type, and for n=2 , there is one more class of transposed Poisson structures on Tₙ(F) . We also show that, up to isomorphism, the full matrix Lie algebra Mₙ(F) admits only one non-trivial transposed Poisson structure, and it is of Poisson type.